The current version of my paper operationalizing and formalizing preferences that are not totally ordered can probably be pushed out the door now. I'm running or going to run it past two more academic economists whom I know before I submit it to a journal, but that's just pronounced caution, and more concerned with the quality of the exposition than with that of the ideas themselves.

Unfortunately, while I'm reasonably sure that the work is correct, I no longer have a gut sense that it's important. Intellectually, I see this lack of such a sense as stemming from a confluence of three things.

The first two are my extended efforts to understand and to communicate matters clearly; these efforts result in those matters now seeming very clear and thus seeming rather obvious to me. I have to remind myself that it was all very murky when I began.

But, additionally, through my life, I've repeatedly had the experience that I just don't feel the significance of completed work. I'm not sure why. Perhaps it's just constitutional anhedonia. I do know that things such as ceremonies and celebrations don't help.

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I've cobbled-together a sort of cheat-sheet for some of my readers who might not be familiar with some of the notation, mathematical notions, and economics jargon that I use in the paper; I'll make it openly available when I make the paper itself more openly available. (In the mean time, anyone with access to the paper who wants a copy of the cheat-sheet should let me know.) At some point, I hope to write-up a sort-of informal translation of the ideas of the paper into far less technical language.

While I'm trying to get readers to visit the Pictorial Arts I'd like to point to a specific pair of entries, The Great Comic Book Heroes part 1 and part 2, from 9 February.

It was in Jules Feiffer's book, The Great Comic Book Heroes, that Buchanan and later I first encountered an untitled story by Will Eisner earlier published in the spring of 1941. Buchanan writes It showed me what comics could be. My reäction had been much the same. I'd seen some awfully good comic book art before I saw this story — Steranko's three issues of Captain America come immediately to-mind — but I'd just never seen anything like this. My sense of what a comic book could be was deeply changed.

(Later, I found more stories by Eisner, and discovered to my great dismay that Eisner had given the character of the Spirit a black side-kick who was depicted in a profoundly racist manner. I'm glad that that side-kick didn't appear in this story, so that my first exposure to work of such quality wasn't blighted.)

Last year, I posted a 'blog entry recommending that my readers visit Golden Age Comic Book Stories, where are found not just golden age comic book stories, but more generally a great many wonderful examples of the art of illustration.

By way of Golden Age Comic Book Stories, I've been led to another 'blog, the Pictorial Arts, to which I also want to give a strong recommendation. Like Golden Age Comic Book Stories, the Pictorial Arts features many examples of outstanding illustration. The Pictorial Arts differs in various respects. Most strikingly, its owner, Thomas Haller Buchanan, writes something of what the illustrations (and often the illustrators themselves) have meant to him, the rôle that they have played in his life.

Buchanan is himself a professional artist of superior ability; one gets to see some of his work

at another of his 'blogs, People Skills. At the Pictorial Arts he says little about that ability or about that work, but instead writes about work of other artists that he has found compelling, from the time that he was a small child up to the present. One may see not what he can produce, but that he could and can see as an illustrator would, and what he saw and sees that made him aspire to become an artist himself.

One of the things that I respect about Buchanan is that he posts about the work that he appreciates, regardless of its social standing. But what has me actually following his the Pictorial Arts is that I like so much of the work to which he directs attention. Some of it is by artists whom I have long admired; in some cases it is work that I too first encountered as a child and which made a strong impression on me. In other cases, I'd not seen it at all before I found it in his 'blog.

In ordinary decision theory, the name weak preference is used for a relation that could be defined as the complement of the inverse of strict preference, or as the union of strict preference with indifference. In ordinary decision theory, these two are equivalent. Typical symbols used for this relationship are ≽, ≿ and ⪰.

In my paper, I noted the conventional conception of weak preference as the aforementioned union; later, I defined it for my purposes such that

(X₁ ≽ X₂) ≡ [{X₁} ⊆ C({X₁, X₂})]

which is the complement of the inverse of strict preference.

Well, I've decided that I was just asking for trouble using that name and that symbol, because people would have trouble not thinking of it as the union of strict preference with indifference, and thence think that a distinct relation of indecision is precluded a priori. So I've switched to the name non-rejection and the symbol ⊀.

There will probably still be people who ask how this relation differs from that of weak preference, but that will be more an expression of their cleverness than of their confusion, and it will be easier to offer an explanation how the relation could be seen as weak preference, how it should not be seen as weak preference. (I may try to squeeze some preëmptive discussion into the paper, though I am bumping-up against size limits.)

Addendum (2009:04/18): I added a preëmptive discussion, so that even fewer people will get confused.

As noted earlier, I've been reading Subjective Probability: The Real Thing by Richard C. Jeffrey. It's a short book, but I've been distracted by other things, and I've also been slowed by the condition of the book; it's full of errors. For example,

It seems evident that black ravens confirm (H) All ravens are black and that nonblack nonravens do not. Yet H is equivalent to All nonravens are nonblack.

Uhm, no: (X ⇒ Y) ≡ (¬X ∨ Y) = (Y ∨ ¬X) = (¬¬Y ∨ ¬X) = [¬(¬Y) ∨ ¬X] ≡ (¬Y ⇒ ¬X) In words, that all ravens are black is equivalent to that all non-black things are non-ravens.[1]

The bobbled expressions and at least one expositional omission sometimes had me wondering if he and his felllows were barking mad. Some of the notational errors have really thrown me, as my first reäction was to wonder if I'd missed something.

Authors make mistakes. That's principally why there are editors. But it appears that Cambridge University Press did little or no real editting of this book. (A link to a PDF file of the manuscript may be found at Jeffrey's website, and used for comparison.) Granted that the book is posthumous, and that Jeffrey was dead more than a year before publication, so they couldn't ask him about various things. But someone should have read this thing carefully enough to spot all these errors. In most of the cases that I've seen, I can identify the appropriate correction. Perhaps in some cases the best that could be done would be to alert the reader that there was a problem. In any case, it seems that Cambridge University Press wouldn't be bothered.

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[1]The question, then, is of why, say, a red flower (a non-black non-raven) isn't taken as confirmation that all ravens are black. The answer, of course, lies principally in the difference between reasoning from plausibility versus reasoning from certainty.

After he read my paper, Anthony told me something that I already knew — that the Discussion section was brief, and the Conclusion sudden. I had been both sick of working on the paper, and having trouble thinking about it in natural language. So those parts were… lacking. Anthony's gentle remarks increased my sense that they were inadequate.

I have expanded and reörganized the Discussion section (cannibalizing part of the Conclusion), and added to the Future Work section between it and the Conclusion. In that context, the Conclusion should seem less sudden, and I have added some thoughts to it (as well as having taken one from it).

Anthony also suggested that the paper could be made more accessible by discussion of the historical background of the problem, and of real-world examples. But, as I told him, I fear to alienate experts by such discussion; and I have since learned that I am already bumping-up against the size-limits for a submission to the journal of my choice.

Anyway, the latest version of my paper is at

On the title page of a translation of one of my father's books, I read

Aus dem Amerikanischen

Mind you that no elevators, automobiles, or bums appear in the book, and discussion probably doesn't get to a thousand million of anything. Perhaps a motion is tabled.

The mathematical expressions that appear (tiled) in the background of this 'blog; are from a paper on which I have been working (off-and-on) over a long time. I'm far from perfectly happy with the present state of the paper, but I've finally put-together something like a complete draft of it, in PDF, at

There are some temporary issues with presentation of this draft:

• The layout needs to be fixed, by the insertion of page breaks, so that things such as section headings are pushed to a next page, rather than orphaned.
• The OpenOffice formula editor does not support use of the relational symbols ≻, ≽, ≿, or ⪰. (For now, I am representing strict preference with pref and weak preference with wpref; later, I will output the paper as LAΤΕΧ and then tweak the formulæ to give me ≻ for strict preference and one of the other three for weak preference.)

At this point, I welcome comments, from experts and from non-experts, both on the underlying content and on how I have expressed myself.

Up-Date (2009:04/08): Professor Gamst of UCSD caught an error in what had been formula (10). It was easily patched. I have up-dated the on-line version of the paper.

Yester-day, I again encountered the slogan No Blood for Oil!, made popular in the run-up to the invasion of Iraq.

I greatly doubt that the people who embrace this slogan have much thought about what it would really mean to forswear the use of violence over economic resources. Only a tiny minority are truly prepared to do that.

This proposition should be obvious in the case of those who want the State to actively participate in decisions about the allocation of resources. The point in having the State determine what quantities will be produced or to whom or to what production will go, or at what prices goods or services will be sold is to use violence or a threat of violence, effected by police and by prison guards. Were the economic administration to be by friendly persuasion, it could be done without the State.

Removing the State as an active participant doesn't utterly remove violence from the equation. If one believes that individuals or communities may forceably defend acquisition, retention, or distribution of goods or of services, then one accepts the use of violence over economic resources. It doesn't matter whether the forceable defense is provided by the State, by private protection agencies, by mobs, or by rugged individualists.

So if one believes that the state should provide the poor with home heating oil, or control gasoline prices, or if one believes in forceably defendable private property in petroleum or in forceably defendable anarcho-socialistic management of petroleum, then one believes in trading blood for oil.

In order to genuinely reject such an exchange, one would have to be truly and utterly pacifistic about petroleum, as are the Amish (albeït that a petroleum pacifist might be violent about other things).

Now, I surely don't claim that the United States should ever use its military in an attempt to secure foreign sources of goods or of services. (We can set aside debate over what the actual relationship were of the invasion of Iraq to American dependence upon Middle Eastern petroleum.) But simple-minded slogans and ad hoc moralizations don't typically propel discourse or move convictions in a humane direction.

Years ago, a friend of mine used to regularly listen to right-wing talk radio. (I imagine that he still does.) I was often a passenger in his car, and there usually had to listen to this programming as well. What I heard drove me up a wall. These commentators didn't usually target people with whose views I agreed, but they routinely misrepresented the arguments that were used by their opponents, made ridiculous universalizations or near-universalizations about the motivations of these opponents, and pretended that the only alternatives to the views of the political left were those of the political right. And the abiding emotion was hate.

For the past few days, I have been visiting my parents. Nearly every evening, they watch MSNBC, and I catch some of it whenever I visit them. What I hear drives me up a wall. The commentators of MSNBC don't usually target people with whose views I agree, but they routinely misrepresent the arguments that have been used by their opponents, make ridiculous universalizations or near-universalizations about the motivations of these opponents, and pretend that the only alternative to the views of the political right are those of the political left. And the abiding emotion is hate.

For example, during this latest visit, I heard Rachel Maddow mocking William Kristol as ostensibly claiming a few weeks into the invasion of Iraq that the war was won, when what Kristol had actually said was that every battle had been decisively won. Were I now to claim that, a few weeks into the American Civil War, every battle had been decisively won by the Confederacy, I would plainly not be claiming that the Confederacy had won the war.

(Maddow was more generally concerned to pretend that the neoconservatives were trying to reposition and to repackage themselves as supporters of the war policy of the Obama Administration. The truth is that, in actual practice, this policy far more closely resembles that of the later Bush Administration than it does the policy described during the Obama candidacy. The neoconservatives, then, don't have to reposition much, though they plainly need to repackage if they are to regain active influence, since their persons and past organizations are anathematized.)

On top of being bothered by all this hate and misrepresentation in-and-of-itself, I am bothered that my father seems to be at least amused by this rubbish, and that my mother sort-of waves-away the fact that there's a stream of misrepresentation, and refuses to acknowledge that the hate is on a par with that of right-wing talk radio.

I end-up closing myself into the principal guest room, away from the television but also then away from my parents.

Amendment (2009:04/10): My father stated, last night, that while my mother likes Rachel Maddow, he finds Maddow unpleasant. Now, if only he would reject some of the other folk on MSNBC.